If the Perimeter of a Semi-Circle is 4π + 8, What is the Area of the GMAT Problem Solving

Question: If the perimeter of a semi-circle is 4π + 8, what is the area of the semi-circle?

1. 16π
2. 8π
3. 4π
4. 8
5. 4

Correct Answer: B

Solution and Explanation
Approach Solution 1:
This question has only one approach.

Given to us that the perimeter of a semicircle is 4π + 8. It has asked to find out the area of that semi-circle.
This is a question from the area and volume topic.
It should be known that a semi-circle is half part of the circle.
The area of a circle is, therefore the area of a semi-circle that will be half of the area of a circle.
The perimeter of a circle is 2πr. The perimeter of a semicircle will be half of that of a circle + the diameter of the circle. We are given that the perimeter of the semicircle is 4π + 8
Let r be the radius of the semicircle.
Πr + 2r = 4π + 8
r(π+2) = 4(π+2)
r =4
Now we know the radius of the semicircle.
It has asked to find out the area of the semicircle.
The area of the circle will be π\(r^2\)
The area of the semi-circle will be π\(r^2\)/2 .
Putting the values in the equation,
Area of semicircle = π(\(4^2\))/2
= π 16/2
= 8π
Therefore the correct answer will be option B.

“If the perimeter of a semi-circle is 4π + 8, what is the area of the”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.“

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